2012/10/15 by Haotian Wu, Wu, Haotian
Mathematics · Physics and Astronomy · #53C44 (Primary) 35K59 (Secondary) #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1210.4089
openalex publication_date 2012/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In each dimension N≥ 3 and for each real number λ≥ 1, we construct a family of complete rotationally symmetric solutions to Ricci flow on ℝN which encounter a global singularity at a finite time T. The singularity forms arbitrarily slowly with the curvature blowing up arbitrarily fast at the rate (T-t)-(λ+1). Near the origin, blow-ups of such a solution converge uniformly to the Bryant soliton. Near spatial infinity, blow-ups of such a solution converge uniformly to the shrinking cylinder soliton. As an application of this result, we prove that there exist standard solutions of Ricci flow on ℝN whose blow-ups near the origin converge uniformly to the Bryant soliton.